One of the current words used to describe that feeling is "burn out." In other times it was just called being spiritually exhausted, tired or weary. There are a myriad of camps and retreat centers which address nothing else.
Why do you suppose we have fallen prey to this particular malady so frequently today?
My best guess is that many of us who are Christians have lost sight of the real goal. Human beings often need to be able to have an end in sight if we are to retain our enthusiasm. The work of Christian service is never easy. It is often filled with disappointment and hardship. Without a clear view of a finish line, the race becomes too difficult. The Apostle Paul could speak of finishing the race as he neared the end of his life because he knew where the finish line was. He had continued to run, in good times and in bad, because the goal was never in doubt.
Paul also knew how difficult the race could be. So the determined apostle also encouraged the runners with words like, "But as for you, brethren, do not grow weary of doing good" (2 Thessalonians 3:13 NASB). He also encouraged the Christians of Galatia with these words: "Let us not lose heart in doing good, for in due time we will reap if we do not grow weary" (Galatians 6:9).
Jesus spoke of being "weary and heavy-laden" with sin and teachings that exhausted and defeated them; he promised his followers relief and blessing (Matthew 11:28). Paul wrote to those who were worn out doing of good. We will reap in due time if we do not exit the race. The light at the end of the tunnel, the finish line, the reward for continuing, are all more than phrases to be quoted; they are also promises from God Himself. The writer of Hebrews continues this same encouragement with these words: "For consider Him who has endured such hostility by sinners against Himself, so that you will not grow weary and lose heart" (Hebrews 12:3). Keep Jesus before you as an antidote against that weariness and the resultant hopelessness of forgetting your goal.
While looking to the finish and contemplating the reward is certainly motivating, we must never forget that the deeper motive of our "doing good." That cardinal motive of all good things must be love. The Revelation calls Christians to "perseverance and endurance." Jesus also reminds us in his message to the churches in the book of Revelation that perseverance and endurance are not enough. God's Son reminded the church in Ephesus of this truth:
... you have perseverance and have endured for My name's sake, and have not grown weary. But I have this against you, that you have left your first love. Therefore remember from where you have fallen, and repent and do the deeds you did at first; or else I am coming to you and will remove your lampstand out of its place—unless you repent' (Revelation 2:3-5).
Run the race with perseverance.
Run and do not lose heart.
Run in expectation of the finish.
Run always compelled by love!